R Tools for Expolratory Data Analysis: Tibbles, data manipulation and introduction to graphics

Background

What is the purpose of these notes?

Provide an overview of:
- Tibbles,
- data manipulation,
Introduce various graphics tricks.
You don’t have to learn everything in this handout, but can use it sort of as a cheat-sheet when you work on your own data. Still, it’s good to walk through it.

Installing and loading packages

Just like every other programming language you may be familiar with, R’s capabilities can be greatly extended by installing additional “packages” and “libraries”.

To install a package, use the install.packages() command. You’ll want to run the following commands to get the necessary packages for today’s lab:

install.packages("tidyverse")
install.packages("ggplot2")
install.packages("knitr")

You only need to install packages once. Once they’re installed, you may use them by loading the libraries using the library() command. For today’s lab, you’ll want to run the following code

library(tidyverse)

── Attaching packages ─────────────────────────────────────── tidyverse 1.3.0 ──

✓ ggplot2 3.3.3     ✓ purrr   0.3.4
✓ tibble  3.0.4     ✓ dplyr   1.0.3
✓ tidyr   1.1.2     ✓ stringr 1.4.0
✓ readr   1.4.0     ✓ forcats 0.5.1

── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
x dplyr::filter() masks stats::filter()
x dplyr::lag()    masks stats::lag()

library(knitr)

library(ggplot2) # graphics library

Context

As we learned in this week’s lectures, Exploratory Data Analysis (EDA) is a process, a state of mind, and for it you need a few tools and pro-tips. This handout provides some of those.

Getting started: birthwt dataset

We’re going to start by operating on the birthwt dataset from the MASS library
Let’s get it loaded and see what we’re working with. Remember, loading the MASS library overrides certain tidyverse functions. We don’t want to do that. So when we need something from MASS we’ll extract that dataset or function directly.

birthwt <- MASS::birthwt

tibbles

tibbles are nicer data frames
You may find it more convenient to work with tibbles instead of data frames
In particular, they have nicer and more informative default print settings
The dplyr functions we’ve been using are very nice because they map tibbles to other tibbles.

birthwt <- as_tibble(birthwt)
birthwt

# A tibble: 189 x 10
     low   age   lwt  race smoke   ptl    ht    ui   ftv   bwt
   <int> <int> <int> <int> <int> <int> <int> <int> <int> <int>
 1     0    19   182     2     0     0     0     1     0  2523
 2     0    33   155     3     0     0     0     0     3  2551
 3     0    20   105     1     1     0     0     0     1  2557
 4     0    21   108     1     1     0     0     1     2  2594
 5     0    18   107     1     1     0     0     1     0  2600
 6     0    21   124     3     0     0     0     0     0  2622
 7     0    22   118     1     0     0     0     0     1  2637
 8     0    17   103     3     0     0     0     0     1  2637
 9     0    29   123     1     1     0     0     0     1  2663
10     0    26   113     1     1     0     0     0     0  2665
# … with 179 more rows

Note: If you want to import data directly into tibble format, you may use read_delim() and read_csv() instead of their base-R alternatives. Even though we started with the base alternatives, I recommend using these improved import commands going forward.

Renaming the variables

The dataset doesn’t come with very descriptive variable names
Let’s get better column names (use help(birthwt) to understand the variables and come up with better names)

colnames(birthwt)

 [1] "low"   "age"   "lwt"   "race"  "smoke" "ptl"   "ht"    "ui"    "ftv"  
[10] "bwt"

# The default names are not very descriptive

colnames(birthwt) <- c("birthwt.below.2500", "mother.age", 
                       "mother.weight", "race", "mother.smokes", 
                       "previous.prem.labor", "hypertension", 
                       "uterine.irr", "physician.visits", "birthwt.grams")

# Better names!

An alternative renaming approach: the `rename()` command

rename operates by allowing you to specify a new variable name for whichever old variable name you want to change.

rename(new variable name = old variable name)

# Reload the data again
birthwt <- as_tibble(MASS::birthwt)

birthwt <- birthwt %>%
  rename(birthwt.below.2500 = low, 
         mother.age = age,
         mother.weight = lwt,
         mother.smokes = smoke,
         previous.prem.labor = ptl,
         hypertension = ht,
         uterine.irr = ui,
         physician.visits = ftv,
         birthwt.grams = bwt)

colnames(birthwt)

 [1] "birthwt.below.2500"  "mother.age"          "mother.weight"      
 [4] "race"                "mother.smokes"       "previous.prem.labor"
 [7] "hypertension"        "uterine.irr"         "physician.visits"   
[10] "birthwt.grams"

Note that in this command we didn’t rename the race variable because it already had a good name.

Renaming the factors

All the factors are currently represented as integers
Let’s use the mutate(), mutate_at() and recode_factor() functions to convert variables to factors and give the factors more meaningful levels

birthwt <- birthwt %>%
  mutate(race = recode_factor(race, `1` = "white", `2` = "black", `3` = "other")) %>%
  mutate_at(c("mother.smokes", "hypertension", "uterine.irr", "birthwt.below.2500"),
            ~ recode_factor(.x, `0` = "no", `1` = "yes"))

birthwt

# A tibble: 189 x 10
   birthwt.below.2… mother.age mother.weight race  mother.smokes
   <fct>                 <int>         <int> <fct> <fct>        
 1 no                       19           182 black no           
 2 no                       33           155 other no           
 3 no                       20           105 white yes          
 4 no                       21           108 white yes          
 5 no                       18           107 white yes          
 6 no                       21           124 other no           
 7 no                       22           118 white no           
 8 no                       17           103 other no           
 9 no                       29           123 white yes          
10 no                       26           113 white yes          
# … with 179 more rows, and 5 more variables: previous.prem.labor <int>,
#   hypertension <fct>, uterine.irr <fct>, physician.visits <int>,
#   birthwt.grams <int>

Recall that the syntax ~ recode_factor(.x, ...) defines an anonymous function that will be applied to every column specfied in the first part of the mutate_at() call. In this case, all of the specified variables are binary 0/1 coded, and are being recoded to no/yes.

Summary of the data

Now that things are coded correctly, we can look at an overall summary

summary(birthwt)

 birthwt.below.2500   mother.age    mother.weight      race    mother.smokes
 no :130            Min.   :14.00   Min.   : 80.0   white:96   no :115      
 yes: 59            1st Qu.:19.00   1st Qu.:110.0   black:26   yes: 74      
                    Median :23.00   Median :121.0   other:67                
                    Mean   :23.24   Mean   :129.8                           
                    3rd Qu.:26.00   3rd Qu.:140.0                           
                    Max.   :45.00   Max.   :250.0                           
 previous.prem.labor hypertension uterine.irr physician.visits birthwt.grams 
 Min.   :0.0000      no :177      no :161     Min.   :0.0000   Min.   : 709  
 1st Qu.:0.0000      yes: 12      yes: 28     1st Qu.:0.0000   1st Qu.:2414  
 Median :0.0000                               Median :0.0000   Median :2977  
 Mean   :0.1958                               Mean   :0.7937   Mean   :2945  
 3rd Qu.:0.0000                               3rd Qu.:1.0000   3rd Qu.:3487  
 Max.   :3.0000                               Max.   :6.0000   Max.   :4990

A simple table

Let’s use the summarize() and group_by() functions to see what the average birthweight looks like when broken down by race and smoking status. To make the printout nicer we’ll round to the nearest gram.

tbl.mean.bwt <- birthwt %>%
  group_by(race, mother.smokes) %>%
  summarize(mean.birthwt = round(mean(birthwt.grams), 0))

`summarise()` has grouped output by 'race'. You can override using the `.groups` argument.

tbl.mean.bwt

# A tibble: 6 x 3
# Groups:   race [3]
  race  mother.smokes mean.birthwt
  <fct> <fct>                <dbl>
1 white no                    3429
2 white yes                   2827
3 black no                    2854
4 black yes                   2504
5 other no                    2816
6 other yes                   2757

Questions you should be asking yourself:
- Does smoking status appear to have an effect on birth weight?
- Does the effect of smoking status appear to be consistent across racial groups?
- What is the association between race and birth weight?

A simple reshape

Some of these questions might be easier if we had the data in a wide rather than a long format. Here’s how we can do that with the spread() function from tidyr
The basic spread() call is spread(data, key, value)

tbl.mean.bwt %>% spread(mother.smokes, mean.birthwt)

# A tibble: 3 x 3
# Groups:   race [3]
  race     no   yes
  <fct> <dbl> <dbl>
1 white  3429  2827
2 black  2854  2504
3 other  2816  2757

What if we wanted nicer looking output?

Let’s use the header {r, results='asis'}, along with the kable() function from the knitr library

# Save the table from before as a 
# Print nicely
kable(spread(tbl.mean.bwt, mother.smokes, mean.birthwt), 
      format = "markdown")

race	no	yes
white	3429	2827
black	2854	2504
other	2816	2757

kable() outputs the table in a way that Markdown can read and nicely display
Note: changing the CSS changes the table appearance

Example: Association between mother’s age and birth weight?

Is the mother’s age correlated with birth weight?

cor(birthwt$mother.age, birthwt$birthwt.grams)  # Calculate correlation

[1] 0.09031781

Does the correlation vary with smoking status?

birthwt %>%
  group_by(mother.smokes) %>%
  summarize(cor_bwt_age = cor(birthwt.grams, mother.age))

# A tibble: 2 x 2
  mother.smokes cor_bwt_age
* <fct>               <dbl>
1 no                  0.201
2 yes                -0.144

Does the association between birthweight and mother’s age vary by race?

birthwt %>%
  group_by(race) %>%
  summarize(cor_bwt_age = cor(birthwt.grams, mother.age))

# A tibble: 3 x 2
  race  cor_bwt_age
* <fct>       <dbl>
1 white      0.166 
2 black     -0.329 
3 other     -0.0293

There does look to be variation, but we don’t know if it’s statistically significant without further investigation.

Graphics in R

We now know a lot about how to tabulate data
It’s often easier to look at plots instead of tables
We’ll now talk about some of the standard plotting options
Easier to do this in a live demo…
Please refer to .Rmd version of lecture notes for the graphics material

Standard graphics in R

Single-variable plots

Let’s continue with the birthwt data from the MASS library.

Here are some basic single-variable plots.

par(mfrow = c(2,2)) # Display plots in a single 2 x 2 figure 
plot(birthwt$mother.age)
with(birthwt, hist(mother.age))
plot(birthwt$mother.smokes)
plot(birthwt$birthwt.grams)

Note that the result of calling plot(x, ...) varies depending on what x is.
- When x is numeric, you get a plot showing the value of x at every index.
- When x is a factor, you get a bar plot of counts for every level

Let’s add more information to the smoking bar plot, and also change the color by setting the col option.

par(mfrow = c(1,1))
plot(birthwt$mother.smokes, 
     main = "Mothers Who Smoked In Pregnancy", 
     xlab = "Smoking during pregnancy", 
     ylab = "Count of Mothers",
     col = "lightgrey")

(much) better graphics with ggplot2

Introduction to ggplot2

ggplot2 has a slightly steeper learning curve than the base graphics functions, but it also generally produces far better and more easily customizable graphics.

There are two basic calls in ggplot:

qplot(x, y, ..., data): a “quick-plot” routine, which essentially replaces the base plot()
ggplot(data, aes(x, y, ...), ...): defines a graphics object from which plots can be generated, along with aesthetic mappings that specify how variables are mapped to visual properties.

library(ggplot2)

plot vs qplot

Here’s how the default scatterplots look in ggplot compared to the base graphics. We’ll illustrate things by continuing to use the birthwt data from the MASS library.

with(birthwt, plot(mother.age, birthwt.grams))  # Base graphics

qplot(mother.age, birthwt.grams, data=birthwt)  # using qplot from ggplot2

I’ve snuck the with() command into this example. with() allows you to use the variables in a data frame directly in evaluating the expression in the second argument.

Remember how it took us some effort last time to add color coding, use different plotting characters, and add a legend? Here’s the qplot call that does it all in one simple line.

qplot(x=mother.age, y=birthwt.grams, data=birthwt,
      color = mother.smokes,
      shape = mother.smokes,
      xlab = "Mother's age (years)",
      ylab = "Baby's birthweight (grams)")

This way you won’t run into problems of accidentally producing the wrong legend. The legend is produced based on the colour and shape argument that you pass in. (Note: color and colour have the same effect. )

ggplot function

The ggplot2 library comes with a dataset called diamonds. Let’s look at it

dim(diamonds)

[1] 53940    10

head(diamonds)

# A tibble: 6 x 10
  carat cut       color clarity depth table price     x     y     z
  <dbl> <ord>     <ord> <ord>   <dbl> <dbl> <int> <dbl> <dbl> <dbl>
1 0.23  Ideal     E     SI2      61.5    55   326  3.95  3.98  2.43
2 0.21  Premium   E     SI1      59.8    61   326  3.89  3.84  2.31
3 0.23  Good      E     VS1      56.9    65   327  4.05  4.07  2.31
4 0.290 Premium   I     VS2      62.4    58   334  4.2   4.23  2.63
5 0.31  Good      J     SI2      63.3    58   335  4.34  4.35  2.75
6 0.24  Very Good J     VVS2     62.8    57   336  3.94  3.96  2.48

It is a data frame of 53,940 diamonds, recording their attributes such as carat, cut, color, clarity, and price.

We will make a scatterplot showing the price as a function of the carat (size). (The data set is large so the plot may take a few moments to generate.)

diamond.plot <- ggplot(data=diamonds, aes(x=carat, y=price))
diamond.plot + geom_point()

The data set looks a little weird because a lot of diamonds are concentrated on the 1, 1.5 and 2 carat mark.

Let’s take a step back and try to understand the ggplot syntax.

The first thing we did was to define a graphics object, diamond.plot. This definition told R that we’re using the diamonds data, and that we want to display carat on the x-axis, and price on the y-axis.
We then called diamond.plot + geom_point() to get a scatterplot.

The arguments passed to aes() are called mappings. Mappings specify what variables are used for what purpose. When you use geom_point() in the second line, it pulls x, y, colour, size, etc., from the mappings specified in the ggplot() command.

You can also specify some arguments to geom_point directly if you want to specify them for each plot separately instead of pre-specifying a default.

Here we shrink the points to a smaller size, and use the alpha argument to make the points transparent.

diamond.plot + geom_point(size = 0.7, alpha = 0.3)

If we wanted to let point color depend on the color indicator of the diamond, we could do so in the following way.

diamond.plot <- ggplot(data=diamonds, aes(x=carat, y=price, colour = color))
diamond.plot + geom_point()

If we didn’t know anything about diamonds going in, this plot would indicate to us that D is likely the highest diamond grade, while J is the lowest grade.

We can change colors by specifying a different color palette. Here’s how we can switch to the cbPalette we saw last class.

cbPalette <- c("#999999", "#E69F00", "#56B4E9", "#009E73", "#F0E442", "#0072B2", "#D55E00", "#CC79A7")
diamond.plot <- ggplot(data=diamonds, aes(x=carat, y=price, colour = color))
diamond.plot + geom_point() + scale_colour_manual(values=cbPalette)

To make the scatterplot look more typical, we can switch to logarithmic coordinate axis spacing.

diamond.plot + geom_point() +
  coord_trans(x = "log10", y = "log10")

Conditional plots

We can create plots showing the relationship between variables across different values of a factor. For instance, here’s a scatterplot showing how diamond price varies with carat size, conditioned on color. It’s created using the facet_wrap(~ factor1 + factor2 + ... + factorn) command.

diamond.plot <- ggplot(data=diamonds, aes(x=carat, y=price, colour = color))

diamond.plot + geom_point() + facet_wrap(~ cut)

You can also use facet_grid() to produce this type of output.

diamond.plot + geom_point() + facet_grid(. ~ cut)

diamond.plot + geom_point() + facet_grid(cut ~ .)

ggplot can create a lot of different kinds of plots, just like lattice. Here are some examples.

Function	Description
`geom_point(...)`	Points, i.e., scatterplot
`geom_bar(...)`	Bar chart
`geom_line(...)`	Line chart
`geom_boxplot(...)`	Boxplot
`geom_violin(...)`	Violin plot
`geom_density(...)`	Density plot with one variable
`geom_density2d(...)`	Density plot with two variables
`geom_histogram(...)`	Histogram

A bar chart

qplot(x = race, data = birthwt, geom = "bar")

Histograms and density plots

base.plot <- ggplot(birthwt, aes(x = mother.age)) +
  xlab("Mother's age") 
base.plot + geom_histogram()

`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

base.plot + geom_histogram(aes(fill = race))

`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

base.plot + geom_density()

base.plot + geom_density(aes(fill = race), alpha = 0.5)

Box plots and violin plots

base.plot <- ggplot(birthwt, aes(x = as.factor(physician.visits), y = birthwt.grams)) +
  xlab("Number of first trimester physician visits") +
  ylab("Baby's birthweight (grams)")

# Box plot
base.plot + geom_boxplot()

# Violin plot
base.plot + geom_violin()

Visualizing means

Previously we calculated the following table:

tbl.mean.bwt <- birthwt %>%
  group_by(race, mother.smokes) %>%
  summarize(mean.birthwt = round(mean(birthwt.grams), 0))

`summarise()` has grouped output by 'race'. You can override using the `.groups` argument.

tbl.mean.bwt

# A tibble: 6 x 3
# Groups:   race [3]
  race  mother.smokes mean.birthwt
  <fct> <fct>                <dbl>
1 white no                    3429
2 white yes                   2827
3 black no                    2854
4 black yes                   2504
5 other no                    2816
6 other yes                   2757

We can plot this table in a nice bar chart as follows:

# Define basic aesthetic parameters
p.bwt <- ggplot(data = tbl.mean.bwt, 
                aes(y = mean.birthwt, x = race, fill = mother.smokes))

# Pick colors for the bars
bwt.colors <- c("#009E73", "#999999")

# Display barchart
p.bwt + geom_bar(stat = "identity", position = "dodge") +
  ylab("Average birthweight") + 
  xlab("Mother's race") +
  guides(fill = guide_legend(title = "Mother's smoking status")) + 
  scale_fill_manual(values=bwt.colors)

Does the association between birthweight and mother’s age depend on smoking status?

We previously ran the following command to calculate the correlation between mother’s ages and baby birthweights broken down by the mother’s smoking status.

birthwt %>%
  group_by(mother.smokes) %>%
  summarize(cor_bwt_age = cor(birthwt.grams, mother.age))

# A tibble: 2 x 2
  mother.smokes cor_bwt_age
* <fct>               <dbl>
1 no                  0.201
2 yes                -0.144

Here’s a visualization of our data that allows us to see what’s going on.

ggplot(birthwt, 
       aes(x=mother.age, y=birthwt.grams, shape=mother.smokes, color=mother.smokes)) + 
  geom_point() + # Adds points (scatterplot)
  geom_smooth(method = "lm") + # Adds regression lines
  ylab("Birth Weight (grams)") + # Changes y-axis label
  xlab("Mother's Age (years)") + # Changes x-axis label
  ggtitle("Birth Weight by Mother's Age") # Changes plot title

`geom_smooth()` using formula 'y ~ x'

License

This document is created for Math 514, Spring 2021, at Illinois Tech. While the course materials are generally not to be distributed outside the course without permission of the instructor, this particular set of notes is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

This worksheet is extracted from Prof. Alexandra Chouldechova at CMU, under the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Sonja Petrović, Associate Professor of Applied Mathematics, College of Computing, Illinios Tech. Homepage, Email.↩︎

R Tools for Expolratory Data Analysis: Tibbles, data manipulation and introduction to graphics